The invention relates to an apparatus for the elimination of substances from liquids, in particular from blood, comprising a primary circuit for the liquid to be treated, a filter which is integrated therein and at whose secondary side a secondary circuit is connected in which at least one adsorber is arranged, wherein respective pumps are provided in the primary and secondary circuits. In accordance with the invention, an expansion vessel in which liquid of the secondary circuit is discontinuously taken up and output again is integrated in the secondary circuit.